Sure it's possible. It's like when you first install operating system without any additional software. It's running fine (sure depending on hardware, ram,....). But as you add more custom applications and services in time like Antivirus, Firewall, ... then system will became slower.
It's the same with extensions. If you install more of them, they can use more RAM, or even more CPU. Still it's also question of what exactly is extension doing. Some can "only" reserve more RAM, but use CPU time only on user action. Some can interact with pages/tabs, so they will use more of resources. So some you won't even recognize, but some can degrade your performance.
You can also see some of statistics in options. First you need to enable Developer Tools at: "More Tools > Enable developer tools". Then open statistics "Developer Tools > Task Manager".